Acoustic radiation force due to sound beams incident on spherical scatterers in soft tissue-like media

This dissertation presents a theory for acoustic radiation force on a spherical scatterer embedded in a soft elastic medium that supports the propagation of shear waves. Existing theories for acoustic radiation force on a sphere are restricted to a fluid surrounding the sphere. Potential applications reside in biology and medicine. For example, the mechanical properties of soft tissue, in particular its shear stiffness, are a useful proxy for tissue health and can be used for non-invasive tissue characterization. The present work investigates the effect that shear elasticity in the surrounding medium has on the radiation force on an embedded spherical scatterer. The theory is developed in Lagrangian coordinates, instead of Eulerian coordinates that are traditionally used for a fluid surrounding the sphere. It is assumed that a compressional wave is incident on the sphere. Coefficients in the spherical harmonic expansions describing the incident compressional wave field, and the scattered compressional and shear wave fields, are examined in detail. The radiation force is separated into two contributions, one that corresponds to the scattered compressional waves and the other to the scattered shear waves, both of which displace the sphere from its initial position. The compressional wave contribution can be determined analytically, and a variety of material properties for the sphere and incident beam patterns are examined for this contribution. The shear wave contribution has yet to be determined analytically, and is investigated numerically. A third contribution, corresponding to the static deformation of the surrounding medium due to the scattered shear wave, is also investigated numerically. A finite element method is used to determine the full effect of the scattered shear wave on the sphere displacement, and it is found that effects due to the scattered shear wave may be of the same order as those due to the scattered compressional wave.